Unfortunately the past projections for EUV have always been overly optimistic, so it's difficult for me to believe that all of the known (let alone the ones we don't know about) barriers to successful cost effective implementation of volume manufacturing with EUV lithography are going to be resolved in the next two years.

It seems to me given the current 13.5 nm wavelength, the modest NA allowed by the current reflective optics, optical flare and shot noise, resist edge roughness, and other image degrading factors, EUV with single patterning will be lucky to achieve one useful node. Then what? Knowing what we know today we might have been better off taking the hit a couple of years ago and putting more resources into optimizing BEUV (beyond EUV, 6.7 nm wavelength). It's still possible that after all this time and money 13.5 nm wavelength EUV could ultimately be seen as limited just as 157 nm and X-ray lithography technologies were before and simply abandoned.

It might be currently 30 targeting 80 WPH for 15 mJ/cm2, which is the current reference dose for a lot of resist characterization. But if the minimum dose needs to be over 60 mJ/cm2, for a chip containing billions of 20 nm contacts or line cuts, then the WPH target is not met. The minimum dose doubles with each successive node.

Zeiss reported at SPIE 2013 the current EUV multilayer for the optics is limited near 13-14 nm half-pitch, which could be 7 nm or 10 nm logic or in between. So if this part of the infrastructure is not changed in time, it's a limit on EUV single exposure.

DSA is still pretty early in the development process. It is a very interesting alternative but still a long way off.

The key question really is what throughput is EUV going to hit and when. In the simulations I have run EUV at 50 wph is already less expensive than triple pattering let alone quadruple patterning. ASML is forecasting 88 wph next year so if they meet that EUV could potentially be a 10nm alternative in a year.

I don't expect EUV to need double patterning at 10nm, certainly not for logic.

The cost of EUV is much lower than the cost of quadruple patterning at any reasonable throughput.

At some point in the future the cost of EUV could be cheaper than quadruple patterning. But when will that be? What throughput is reasonble and what will it take to get there? I would not make such a blanket statement today. The whole EUV infrastructure will still be quite expensive in the near term. And I think there are still too many unknowns today to declare that EUV lithography will be cost competitive by a certain date. I don't think its guaranteed. Obviously each company will have to decide what it's costs will be with either scenerio, which will depend on many factors. Whether or not EUV will be ready for a 10 nm node remains to be seen.

I am not sure where you get the EUV energy (dose) estimates. What you see in publications or the reports from ASML or IMEC (15-20 mJ/cm2) is not going to work in the high-volume manufacturing, with billions of features requiring a certain dose precision. More like 60 and going higher. It makes no practical difference from multiple patterning because, for a smaller node, this dose has to go up, similar impact to increasing ArFi exposures.

The cost of EUV is much lower than the cost of quadruple patterning at any reasonable throughput.
The energy required for an EUV exposure is more than the energy for a ArFi exposure but is less than the two ArFi exposures plus depositions and etches required for double patterning and is much lower than what is required for quadruple patterning.
Quadruple patterning at 10nm could require up to five cut masks and that would be a huge cost problem.

If the quadruple patterning is double the cost but 4x the density from single patterning, it still continues cost reduction. Even with EUV, the energy cost is high, so there is no benefit at that point over multiple patterning.